Avram Grant is expected to be named as West Ham's new manager on Thursday.
The Hammers revealed on Wednesday afternoon they would announce Gianfranco Zola's successor 'within 24 hours' with co-chairman David Gold indicating Grant was the preferred choice.
"After an hour, we knew we could work with this manager. We are very optimistic," Gold told BBC Sport.
"I think it's time for the football club to get some stability with people that have been there, done that and got the T-shirt."
He added: "The bottom line is the relationship between the manager and the chairman is critical.
"In our case it's two chairmen (Gold and David Sullivan) so it's even more difficult as you need to have a relationship between three people."
Croatia coach Slaven Bilic, Blackpool boss Ian Holloway, Cardiff manager Dave Jones and Sam Allardyce of Blackburn had also been linked with the job.
Zola steered West Ham to safety on 35 points, enough to keep them one place above the relegation zone, but was sacked soon after.
The Hammers were saved by the shortcomings of the teams below them as much as their own efforts, forcing Gold and fellow co-chairman Sullivan to act.
Grant took Chelsea to the Champions League final in 2008 but was shown the door after the defeat by Manchester United. The 55-year-old Israeli returned to the Barclays Premier League with Portsmouth last year, first as director of football and then as manager following the removal of Paul Hart.
His success in leading Portsmouth, who were subsequently placed into administration, to the FA Cup final amid horrendous financial constraints won universal approval.
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